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In ground-penetrating radar imaging, the classic back-projection (BP) algorithm has an excellent reputation for imaging in layered mediums with convenience and robustness. However, the classic BP algorithm is time consuming and with a lot of artifacts, which have adverse effects on the following work like detection and recognition. A novel BP algorithm, which is both fast and with good effect of suppressing artifacts, is proposed in this letter. At first, an approved approximation method is used to calculate the position of refraction point with remarkable speed and satisfactory accuracy. Then, a lookup table is used to reduce the redundancy in classic BP algorithm. In order to achieve effective artifact suppression, a cross-correlation-based method is introduced. Experimental results of field data present the superiority of the proposed BP algorithm over its classic counterpart both in operation speed and artifact suppression.